Method and system for determining depth distribution of radiation-emitting material located in a source medium and radiation detector system for use therein

ABSTRACT

A method, system and a radiation detector system for use therein are provided for determining the depth distribution of radiation-emitting material distributed in a source medium, such as a contaminated field, without the need to take samples, such as extensive soil samples, to determine the depth distribution. The system includes a portable detector assembly with an x-ray or gamma-ray detector having a detector axis for detecting the emitted radiation. The radiation may be naturally-emitted by the material, such as gamma-ray-emitting radionuclides, or emitted when the material is struck by other radiation. The assembly also includes a hollow collimator in which the detector is positioned. The collimator causes the emitted radiation to bend toward the detector as rays parallel to the detector axis of the detector. The collimator may be a hollow cylinder positioned so that its central axis is perpendicular to the upper surface of the large area source when positioned thereon. The collimator allows the detector to angularly sample the emitted radiation over many ranges of polar angles. This is done by forming the collimator as a single adjustable collimator or a set of collimator pieces having various possible configurations when connected together. In any one configuration, the collimator allows the detector to detect only the radiation emitted from a selected range of polar angles measured from the detector axis. Adjustment of the collimator or the detector therein enables the detector to detect radiation emitted from a different range of polar angles. The system further includes a signal processor for processing the signals from the detector wherein signals obtained from different ranges of polar angles are processed together to obtain a reconstruction of the radiation-emitting material as a function of depth, assuming, but not limited to, a spatially-uniform depth distribution of the material within each layer. The detector system includes detectors having different properties (sensitivity, energy resolution) which are combined so that excellent spectral information may be obtained along with good determinations of the radiation field as a function of position.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application is based on U.S. provisional patent applicationentitled “Augmented Reality Radiation Display System and In SituSpectrometry Method for Determining the Depth Distribution ofRadionuclides” filed Apr. 16, 1999 and having U.S. Ser. No. 60/129,837.

GOVERNMENT RIGHTS

[0002] This invention was made with government support under ContractNo. DE-AC05-76OR00033 awarded by the U.S. Department of Energy. Thegovernment has rights in the invention.

TECHNICAL FIELD

[0003] This invention relates to methods and systems for determiningdepth distribution of radiation-emitting material located in a sourcemedium and radiation detector system for use therein.

BACKGROUND ART

[0004] In principle, in situ gamma-ray spectrometry determines thequantities of radionuclides in some source medium with a portabledetector. In comparison, the more established method of laboratorygamma-ray spectroscopy consists of taking small samples of the mediuminto the laboratory for gamma-ray analysis. In situ gamma-rayspectrometry characterizes a larger volume of material, requires lesstime to determine accurate radionuclide concentrations, and minimizesworker doses and the risk of radioactive contamination. The mainlimitation of in situ gamma-ray spectrometry lies in determining thedepth distribution of radionuclides.

[0005] In general, radionuclide depth distributions aid conventional insitu gamma-ray spectrometry in determining accurate radionuclideinventories and surface does rates from individual radionuclides. Depthdistributions also represent reliable data for radionuclide transportstudies. Indications of neutron or energetic charged particle fluxes canresult from determinations of the activation as a function of materialdepth. For decontamination and decommissioning activities, theradionuclide depth distribution determines the amount of material thatmust be remediated to satisfy the release limits.

[0006] To date, three in situ gamma-ray spectroscopic methods have beenused to determine the depth distribution of radionuclides in soil andare presented hereinbelow. These three in situ methods are based onmultiple photopeak responses, the photopeak-to-valley ratio, and theattenuation of a lead plate as illustrated in FIGS. 1a and 1 b. Eachmethod requires a priori assumptions of the depth distribution functionand uses a gamma-ray spectrometer. Spectrometers allow the users todecipher the energies of gamma-ray emissions, a necessity fordetermining the specific radioisotope present. In addition to usuallyassuming a uniform soil density with depth, all three approaches fordetermining depth distributions also assume a spatially uniformradionuclide distribution. All three in situ methods require a prioriassumptions of the functional form for the depth distribution. Themultiple photopeak and peak-to-valley methods only have the ability ofdetermining a single depth parameter. An exception exists if theradionuclide of interest emits three or more significant gamma-rays,decently separated in energy, and if the spectrometer used hassufficient energy resolution to identify and separate each gamma-rayemission. In such cases, the multiple photopeak method could determineone fewer number of depth parameters than the number of significantgamma-rays emissions. The subsurface maxima exhibited by aged ¹³⁷Csfallout in soil are best described by at least two depth parameters andcan not be adequately characterized by a single depth parameter. Table 1summarizes the advantages and disadvantages of the three in situmethods. TABLE 1 GENERAL ADVANTAGES AND DISADVANTAGES OF THE THREESTANDARD IN SITU METHODS FOR DETERMINING RADIONUCLIDE DEPTHDISTRIBUTIONS Method Advantages Disadvantages Multiple PhotopeakRequires a single Requires at least two measurement at each sitesignificant gamma-ray emissions Gamma-ray emissions must have a largeseparation in energy Depth information limited by the gamma-ray decayscheme of the radionuclide of interest Multiple measurements at the samesite yield no additional depth information Peak-to-Valley Ratio Requiresonly one Sensitive to significant interference in gamma-ray emissioncomplex gamma-ray fields Requires a single Multiple measurement at eachsite measurements at the same site yield no additional depth informationLead Plate Requires only one Requires multiple significant measurementsgamma-ray emission at each site Multiple measurements Adds weight to atthe same site the portable system yield additional depth information

[0007] In addition to the three in situ methods for determining depthdistributions, spectroscopic measurements in boreholes have also beenstudied for applications in oil wells. Because boring itself qualifiesas an invasive process, borehole measurements should be considered aquasi-in-situ approach. In addition to increased contamination risks,borehole measurements require boring equipment and custom fabricateddetection equipment (extended cryostat lengths for HPGe detectors).

[0008] Three other imaging techniques include: pinhole collimation,coded aperture imaging, and Compton scatter imaging. The mainlimitation, common to all three of these imaging techniques, is theenergy resolution of the detectors used. These other imaging techniquesutilize position-sensitive detector arrays, which typically are largescintillation crystals with insufficient energy resolution for complexgamma-ray fields. For characterizing low levels of radioactivity,advancements in position-sensitive semiconductor detectors have not yetyielded devices that are large enough for adequate sensitivities oraffordable enough for a rugged and portable in situ system.

[0009] U.S. Pat. No. 4,197,460 to Anger discloses a collimator assemblyused to perform multi-angle nuclear imaging and the results are used toestimate relative depth of objects. Multi-angle display circuits dividethe probe radiation image into different regions.

[0010] U.S. Pat. No. 3,979,594 to Anger discloses how relative positionsof radiation sources at different depths are estimated via a focusedcollimator. Multiple-channel collimators are mentioned as an option tobe used.

[0011] U.S. Pat. No. 5,429,135 to Hawman et al. discloses how a focusingcollimator detects the depth of an organ in nuclear medicine.

[0012] U.S. Pat. No. 5,442,180 to Perkins et al. discloses an apparatusfor determining the concentration of radioactive constituents in testsamples (such as surface soil) by means of a real-time direct readout.

[0013] Other U.S. patents of a more general interest include: U.S. Pat.Nos. 4,394,576; 5,773,829; and 5,870,191.

[0014] The primary measurement problem which is not solved by the priorart is the in situ determination of the depth distribution of gamma-rayemitting radionuclides in source media. Contaminated soil and activatedconcrete are common examples of anthropogenic radionuclides in largearea geometries. For these measurement situations, the gamma-rayspectrum tends to be complex due to the presence ofmultiple-radionuclides (natural or anthropogenic in origin). Therefore,the spectrometers used in the field must possess excellent energyresolution to minimize the deleterious effects of interfering gamma-rayemissions. Other practical issues are that an in situ detection systemshould be portable and rugged. Because it is not uncommon for low levelsof anthropogenic radionuclides to be present in smaller quantities thannatural radionuclides, it is important that the detection system alsopossess a sufficient gamma-ray detection efficiency for reasonablecounting times.

DISCLOSURE OF INVENTION

[0015] An object of the present invention is to provide a method andsystem for determining depth distribution of radiation-emitting materiallocated in a source medium and a radiation detector system for usetherein wherein the invention can be used with respect to any sourcemedium as long as its attenuation properties are insignificant, known,measurable, or estimable in any way.

[0016] Another object of the present invention is to provide a methodand system for determining depth distribution of radiation-emittingmaterial located in a source medium and a radiation detector system foruse therein wherein in situ radiation measurements are performed such asgamma-ray spectrometry and offer a superior ability for characterizingcomplex depth distributions.

[0017] Still another object of the present invention is to provide amethod and system for determining depth distribution ofradiation-emitting material located in a source medium and a radiationdetector system for use therein wherein the radiation-emitting materialis radionuclides.

[0018] Yet still another object of the present invention is to provide amethod and system for determining depth distribution ofradiation-emitting material located in a source medium and a radiationdetector system for use therein wherein conventional radiation detectionequipment can be employed.

[0019] Yet still another object of the present invention is to provide amethod and system for determining depth distribution ofradiation-emitting material located in a source medium and a radiationdetector system for use therein wherein the depth distribution iscalculated without a priori knowledge about the depth distributionswithout required a priori selection of a specific functional form forthe depth distribution and without the need for invasive core samplings.

[0020] In carrying out the above objects and other objects of thepresent invention, a method for determining depth distribution ofradiation-emitting material located in a source medium is provided. Themethod includes detecting radiation emitted by the material withinselected ranges of polar angles relative to a detector axis which issubstantially perpendicular to an outer surface of the source medium toproduce a plurality of corresponding electrical signals. The method alsoincludes processing the plurality of electrical signals to obtain thedepth distribution of the radiation-emitting material in the sourcemedium.

[0021] The radiation may include x-ray emissions and/or gamma-rayemissions.

[0022] The material may be radionuclides or is energized so that thematerial emits the radiation.

[0023] The source medium may be soil or building materials such asconcrete and/or steel.

[0024] The source medium may be an airborne plume.

[0025] The step of detecting is preferably at least partially performedwith a detector having intrinsic efficiency and angular response andwherein the step of processing processes data representing the intrinsicefficiency and the angular response with the electrical signals toobtain the depth distribution.

[0026] In further carrying out the above objects and other objects ofthe present invention, a system for determining depth distribution ofradiation-emitting material located in a source medium is provided. Thesystem includes at least one detector assembly for detecting radiationemitted by the material within selected ranges of polar angles relativeto a detector axis which is substantially perpendicular to an outersurface of the source medium to produce a plurality of correspondingelectrical signals. The system also includes a signal processor forprocessing the plurality of electrical signals to obtain the depthdistribution of the radiation-emitting material in the source medium.

[0027] The detector assembly may include a radiation detector and aradiation shield which surrounds the radiation detector, wherein the atleast one detector assembly is adjustable to allow the radiationdetector to detect radiation within the selected ranges of the polarangles and the radiation shield substantially blocks radiation outsidethe selected ranges of the polar angles.

[0028] The shield may be a collimator which is cylindricallysymmetrical.

[0029] The collimator may include a plurality of collimator pieces whichcan be assembled into a plurality of geometric arrangementscorresponding to the ranges of polar angles.

[0030] The collimator may be adjustable into a plurality of geometricarrangements corresponding to the ranges of polar angles.

[0031] The at least one detector assembly may be a radiationspectrometer.

[0032] The at least one detector assembly may include at least one of anarray of detectors, a position-sensitive detector and a scanningdetector.

[0033] The collimator may be movable relative to the detector.

[0034] For example, the collimator may include at least one collimatorpiece which is pivotally movable relative to the detector.

[0035] A pair of detector assemblies allow the system to focus at aselected depth of the source medium.

[0036] The collimator may be linearly movable relative to the detector.

[0037] The collimator may be cylindrically symmetrical about thedetector.

[0038] The at least one detector assembly could have a relatively narrowfield of view that is capable of being directed at a desired polar anglefor a measurement and is rotatable about the detector axis. The sameeffect can also be accomplished with rotating the entire detectorassembly, with a narrow field of view and at a fixed-polar angle, aboutthe normal of the source surface.

[0039] Still further in carrying out the above objects and other objectsof the present invention, a radiation detector system is provided. Thesystem includes at least one central radiation detector for convertingionizing radiation into a first signal. The system also includes atleast one satellite radiation detector positioned adjacent the at leastone central radiation detector for converting ionizing radiation into atleast one second signal. The system further includes at least oneradiation shield disposed adjacent the at least one satellite radiationdetector to substantially block ionizing radiation originating outside afield of view of the at least one satellite radiation detector. Thefirst signal and the at least one second signal represent a spectralfingerprint of an area and spatial distribution of an ionizing radiationsource within the area.

[0040] The satellite radiation detectors may be spectroscopic radiationdetectors.

[0041] The ionizing radiation may include gamma rays wherein the systemis a position-sensitive, compound gamma ray spectrometer.

[0042] The central radiation detector preferably includes asemiconductor substrate.

[0043] Radionuclides represent one of the most significant contaminationproblems for the Department of Energy (DOE). Implementation of thisinvention would decrease the risk of the public and workers to radiationand significantly reduce the cost and time of radiation characterizationactivities. As a powerful tool for radionuclide characterization andverification of remediation, this invention is immediately applicable tothe widespread radionuclide cleanup activities of soil contamination aswell as activated or contaminated building materials (such as concreteor steel) across the DOE complex and commercial nuclear power industry.This invention could also determine vertical or horizontal distributionsof radionuclides in airborne plumes or be applied to boreholemeasurements for determining radionuclide depth distributions.Modifications could be made for the characterization of contamination inlaboratories and for other geometries, such as tanks, drums, pipes, etc.

[0044] Conventional in situ gamma-ray spectrometry uses an unshieldedgamma-ray detector placed 1 m above the soil surface. This inventionimplements a unique collimator with conventional or unconventionalradiation detection equipment. A cylindrically symmetric collimator ispositioned so that its axis is normal to surface of the area source andsurrounds the detector and allows only those gamma-rays emitted from aselected range of polar angles (measured off the detector axis) to bedetected. Adjustment of the collimator enables the detection ofgamma-rays emitted from a different range of polar angles andpreferential depths. Assuming a spatially uniform radionuclidedistribution (in the plane normal to the collimator axis) within eachdepth increment and any radionuclide depth distribution (uniform orotherwise) within each depth increment, the unattenuated or uncollidedgamma-ray flux from each depth increment can be calculated and pairedwith the intrinsic efficiency and angular response of the detector toyield a detector response matrix over the selected depth increments andrange of measured polar angles. The uncollided or unattenuatedgamma-rays are those gamma-rays which are emitted from a radionuclideand do not interact in the material between the radionuclide and thedetector.

[0045] The present invention is an improvement over the lead platemethod of FIGS. 1a and 1 b. By avoiding the summing effect of large andsmall polar angles from moving a simple lead plate farther from thedetector, the present invention exhibits a smaller measurement error. Inaddition, the present invention's angled edges allow for more effectiveshielding of those radiations emitted outside of the polar angle rangeand allow for a more straightforward response calculation.

[0046] This invention offers superior sensitivity, easier operation, andgreater robustness requiring less maintenance under rugged conditions ascompared with the prior art.

[0047] Each measurement of a particular range of polar angles isperformed with a different combination of the collimator pieces or bysetting a single adjustable collimator to a similar geometry. The matrixequation for determining the detector response for each collimator setupcould take the following form:

m=Hd

[0048] where m is column vector for the detector response or measuredphotopeak count rate at each range of polar angles, H is the detectorresponse matrix for each combination of polar angle and depth incrementand represents the photopeak count rate from a unit radionuclidespecific activity in a specific depth increment for a specificcollimator setup, and d is a column vector for the radionuclide depthdistribution (radionuclide specific activity in units of Bq per gram ofmaterial in each depth increment for example). Calculation of the depthdistribution follows from solution of the following matrix equation:

d=H⁺m

[0049] where H⁺ is the matrix such that H⁺m=H⁺Hd=d (note that H⁺ iscalled the inverse of the detector response matrix, H, when H is asquare matrix such that the column vectors m and d are of the samedimension). Therefore, processing of the measured angular data in myields a reconstruction of the radionuclide distribution with depth, d.

[0050] It should be noted that improvements in the depth distributiondeterminations could be obtained from (a) increasing the collimatedmeasurements to invoke an overdetermined situation (oversampled method),and (b) from simplifying the response matrix by neglecting the elementsof the matrix that are small with respect to the other elements for aparticular polar angle measurement. In addition to analyticalcalculations and actual measurements, the response matrix can also becomputed from Monte Carlo computer simulations.

[0051] The elements of the invention which are new compared to thecurrent prior art are:

[0052] defining independent spatially uniform depth increments each witha uniform or any other depth radionuclide distribution within each depthincrement;

[0053] using a cylindrically symmetric collimator to allow significantdetector photopeak response over a small range of polar angles andnegligible photopeak response for gamma-rays incident on the detector atpolar angle outside of the small range; and

[0054] determining the detector response for a small range of polarangles from a unit radionuclide source in each depth increment (definingthe detector response matrix).

[0055] Instead of using a single gamma-ray spectrometer with severaldifferent collimator setups, simultaneous angular measurements could beperformed with a position sensitive detector, array of detectors, orscanning detectors. Instead of several fixed collimator pieces, a singlemechanically adjustable collimator could achieve the differentcollimator setups.

[0056] The above objects and other objects, features, and advantages ofthe present invention are readily apparent from the following detaileddescription of the best mode for carrying out the invention when takenin connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

[0057]FIGS. 1a and 1 b are cross-sectional views of a prior art in situgamma-ray spectrometry setup with a lead plate located at two differentdistances from the detector, the detector predominately responds tothose gamma-rays emitted from radionuclides located outside the dashedlines; for a lead plate location close to the detector, as shown in FIG.1a, the detector preferentially responds to those radionuclidescontained within the shallower layers of soil; for a large lead plate ata distance from the detector, as shown in FIG. 1b, the detector isshielded from those radionuclides located directly beneath the leadplate, and a larger volume of soil contributes to the detector response;

[0058]FIG. 2 is a cross-sectional schematic view of the in situgamma-ray spectrometry geometry, wherein r is the distance from thedetector to a radionuclide contained within an infinitesimal volume ofsoil in units of cm, θ is the off-axis polar angle of the radionuclidemeasured from the axis of the detector in units of radians, h is theheight of the detector above the soil surface in units of cm, μ_(a) isthe linear gamma-ray attenuation coefficient for air in units of cm⁻¹,dV is an infinitesimal volume of soil, and μ_(s) is the linear gamma-rayattenuation coefficient for soil in units of cm⁻¹;

[0059]FIG. 3 is a cross-sectional view of the limited angle and depth insitu geometries for five polar angle ranges and five soil layers; due tosize limitations, only the right-hand side of the cross-sectional viewis displayed; a true cross-sectional view could also show a mirror imageof the polar angles to the left of the axis (direction normal to thesoil surface); based on uniform (homogenous) distribution of ¹³⁷Cs insoil having typical properties; the numbers represent the percentages ofthe total uncollided gamma-ray flux incident at the detector from eachdepth layer for a particular range of polar angles, the five polar angleranges shown (not to scale) are 0-34°, 34-48°, 48-60°, 60-70°, and70-80°;

[0060]FIG. 4 is a cross-sectional view of a first embodiment of acollimator/detector assembly located on the source medium surface, thosegamma-rays emitted within the collimate region of interest and withinthe polar angle range do not encounter lead attenuation along their pathto the center of the detector crystal; three gamma-ray trajectories aredepicted: a) emitted within the collimated region of interest andincident at the detector within the polar angle range encounters no leadattenuation, b) emitted outside the collimated region of interest withinthe polar angle range encounters lead attenuation, and c) emitted withinthe collimated region of interest and outside the polar angle rangeencounters lead attention;

[0061]FIG. 5 is a cross-sectional view of a second embodiment of acollimator and movable detector assembly; the different polar angleranges are measured by moving the detector to each of the dashedlocations within the cylindrically symmetric collimator; alternativelyeach dashed location may represent a separate positional detector toallow 2-D or 3-D application;

[0062]FIG. 6 is a cross-sectional view of a third embodiment of such anassembly wherein by switching lowest collimator section, the lowestdetector position allows the measurement of those gamma-rays incident atsmall polar angles;

[0063]FIG. 7 is a cross-sectional view of a fourth embodiment of such anassembly wherein the detector is in its uppermost detector position; byremoving the lowest collimator section, this detector position allowsthe measurement of those gamma-rays incident at small polar angles; thedetector is positioned above the smallest polar angle passed by theuppermost collimator opening;

[0064]FIGS. 8a-8 d schematically show three alternativecollimator/detector assembly geometries: FIG. 8a shows a movablecollimator with a fixed detector, FIG. 8b shows a dual detector designwith movable on-axis collimator to allow the system to focus at aparticular depth, FIG. 8c shows a system where the detector can be movedwith respect to a fixed collimator, and FIG. 8d shows a simple pivotingdesign as an alternative to vertical movements of the collimator withrespect to the detector and source surface; and

[0065]FIG. 9 is a top cross-sectional view of a multiple detectorsystem; a larger HPGe detector is surrounded with a ring of CdZnTedetectors; shielding is placed in between each CdZnTe detector to reducethe gamma-ray contributions originating outside a “forward” field ofview.

BEST MODE FOR CARRYING OUT THE INVENTION

[0066] The method and system of the present invention preferably employa unique collimator design used with conventional radiation detectionequipment. The cylindrically symmetric collimators disclosed herein aredesigned to allow only those gamma-rays emitted from a selected range ofpolar angles (measured off the detector axis) to be detected. Thecollimators are positioned with their axes normal to surface of themedia, and multiple collimator measurements detect gamma-rays emittedfrom different ranges of polar angles and preferential depths.

[0067] The method and system of the invention also includes sectioningthe measured medium into several independent depth layers. Althoughother distributions within each depth layer could also be assumed, auniform radionuclide distribution is assigned to each depth layer. Afterthe source medium is sectioned into depth layers, system-of-responseequations are created relating the measured photopeak count rates withthe different collimators to the activities contained within the depthlayers. Solving the system-of-response equations for the in situspectrometer measurements using the different collimators enablesreconstructions of the radionuclide depth distribution. While previousin situ methods rely on a priori assumptions of the depth distributionshape, the approach described herein calculates the depth distributionin a histogram format without fitting the depth distribution to apreassigned function. Because the method and system of the inventiononly requires the net photopeak count rates from the collected gamma-rayspectra, the method and system of the invention are virtually unaffectedby scattered gamma-rays from the radionuclide of interest or from otherradionuclides.

[0068] Theory and Methodology

[0069] Whereas conventional in situ gamma-ray spectrometry uses anunshielded gamma-ray detector positioned 1 m above the soil surface, themethod and system of the present invention implements a uniquecollimator to be used at the surface with conventional in situequipment. A cylindrically symmetric collimator, positioned so that itsaxis is normal to the surface of the area source, surrounds the detectorand allows only those gamma-rays emitted from a selected range of polarangles (measured off the collimator axis) to be detected. Adjustment ofthe collimator enables detection of gamma-rays emitted from a differentrange of polar angles and preferential depths. Processing of the datafrom different angles yields a reconstruction of the radionuclidedistribution with depth. Collimation is used to obtain radionuclidedepth distribution information from in situ gamma-ray measurements.

[0070] Uncollided Gamma-ray Flux Calculations for a UniformlyDistributed Source

[0071] In this section, the total uncollided gamma-ray flux for a singlegamma-ray energy incident at an in situ detector is derived for uniformsource distribution in soil. The specific situations of limiting and thepolar angle as well as limiting the depth of soil are introduced, andtheir impact on the gamma-ray flux is derived. Derivations of in situgamma-ray spectrometry calibration factors have been addressed inseveral publications (Beck et al. 1972; Helfer and Miller 1988; ICRU1994). The geometry of in situ gamma-ray spectrometry is presented inFIG. 2 wherein r is the distance from the surface of the detector to asingle radionuclide contained within an infinitesimal volume of soil inunits of cm, θ is the off-axis polar angle of the radionuclide measuredfrom the axis of the detector in units of radians, and h is the heightof the detector above the soil surface in units of cm.

[0072] As shown in FIG. 2, a cylindrical detector is positioned so itsaxis is normal to the measurement surface. The polar angles are measuredoff the axis of the cylindrical detector and from the center of thedetector crystal. To enable greater counting efficiencies and improvedsystem sensitivity, the collimator design allows contributions from theentire azimuthal field of view. The azimuthal angle is defined as theangle of rotation about the axis of the detector. By allowing a fullazimuthal field of view, larger volumes of source media arecharacterized with each collimator measurement, thereby offering a morerepresentative result as well as reducing the required counting times.

[0073] Computing the total gamma-ray flux at the detector from a volumesource requires triple integration of an infinitesimal volume of soil.Accounting for the gamma-ray attenuation from the soil and air, thetotal uncollided gamma-ray flux becomes: $\begin{matrix}{\varphi_{total}^{uniform} = {\int_{0}^{2\pi}{\int_{0}^{\frac{\pi}{2}}{\int_{h\quad \sec \quad \theta}^{\infty}{\frac{S_{v}}{4\pi \quad r^{2}}^{- {\mu_{s}{({r - {h\quad s\quad {ec}\quad \theta}})}}}^{- {\mu_{a}{({h\quad \sec \quad \theta})}}}r^{2}\sin \quad \theta \quad {r}\quad {\theta}\quad {\phi}}}}}} & (1)\end{matrix}$

[0074] where

[0075] S_(v) is the gamma-ray emission rate per unit volume of soil withunits of γ s⁻¹ cm⁻³

[0076] μ_(s) is the soil attenuation coefficient in units of cm⁻¹,

[0077] μ_(a) is the air attenuation coefficient in units of cm⁻¹, and

[0078] φ is the azimuthal angle in units of radians.

[0079] Breaking Equation (1) into parts, $\begin{matrix}{\frac{S_{v}}{4\pi \quad r^{2}}\quad {represents}\quad {the}\quad {flux}\quad a\quad {distance}\quad r\quad {from}\quad a\quad {point}\quad {source},} \\{^{- {\mu_{s}{({r - {h\quad \sec \quad \theta}})}}}\quad {represents}\quad {the}\quad {soil}\quad {attenuation},} \\{^{{- {\mu_{a}{({h\quad \sec \quad \theta})}}}\quad}\quad {represents}\quad {the}\quad {air}\quad {attenuation},\quad {and}}\end{matrix}$

[0080] r² sin θ dr dθ dφ represents the Jacobian for an infinitesimalvolume of soil, dV. The flux per unit polar angle can be obtained byintegrating Equation (1) with respect to r and φ resulting in:$\begin{matrix}{\frac{\varphi}{\theta} = {\frac{S_{v}}{2\mu_{s}}\sin \quad {\theta ~ \cdot {^{{- \mu_{a}}h\quad \sec \quad \theta}.}}}} & (2)\end{matrix}$

[0081] To obtain the total flux, Equation (2) will be integrated overpolar angle, θ: $\begin{matrix}{{\varphi_{total}^{uniform} = {\frac{S_{v}}{2\mu_{s}}{\int_{0}^{\frac{\pi}{2}}{\sin \quad {\theta \cdot ^{{- \mu_{a}}h\quad \sec \quad \theta}}\quad {{\theta}.}}}}}\quad} & (3)\end{matrix}$

[0082] Making a change of variables, results in: $\begin{matrix}{\varphi_{total}^{uniform} = {\frac{S_{v}}{2\mu_{s}}{\int_{1}^{\infty}{\frac{^{{- \mu_{a}}{h\omega}}}{\omega^{2}}\quad {{\omega}.}}}}} & (4)\end{matrix}$

[0083] where ω=sec θ and sin θ dθ=dω/ω² (knowing dω=sec θ tan θ dθ).

[0084] Using the following definition of the exponential integral forn={0, 1, 2, 3, . . . } and for a real x>0: $\begin{matrix}{{E_{n}(x)} = {\int_{1}^{\infty}{\frac{^{- {xt}}}{t^{n}}\quad {t},}}} & (5)\end{matrix}$

[0085] with t=ω, n=2, and x=μ_(a)h, the total flux for a uniform sourcedistribution becomes: $\begin{matrix}{\varphi_{total}^{uniform} = {\frac{S_{v}}{2\mu_{s}}{{E_{2}( {\mu_{a}h} )}.}}} & (6)\end{matrix}$

[0086] Using the exponential integral recurrence relation for n={1, 2,3, . . . }: $\begin{matrix}{{E_{n + 1}(x)} = {{\frac{1}{n}\lbrack {^{- x} - {x \cdot {E_{n}(x)}}} \rbrack},}} & (7)\end{matrix}$

[0087] with n=1, the total flux for a uniform source distribution cantake a slightly different appearance: $\begin{matrix}{\varphi_{total}^{uniform} = {{\frac{S_{v}}{2\mu_{s}}\lbrack {^{{- \mu_{a}}h} - {\mu_{a}{h \cdot {E_{1}( {\mu_{a}h} )}}}} \rbrack}.}} & (8)\end{matrix}$

[0088] Limited Angle Case

[0089] In this section, a derivation is performed for a case where thecontributions to the uncollided gamma-ray flux are considered only froma reduced range of polar angle. For this limited polar angle case andfor a uniform source distribution, Equation (4) takes the followingform: $\begin{matrix}{\varphi_{limited}^{uniform} = {\frac{S_{v}}{2\mu_{s}}{\int_{\omega_{1}}^{\omega_{2}}{\frac{^{{- {({{- \mu_{a}}h})}}\omega}}{\omega^{2}}\quad {{\omega}.}}}}} & (9)\end{matrix}$

[0090] where ω₁<ω₂ (or θ₁<θ₂). Manipulating the limits of integration,one knows: $\begin{matrix}{{\int_{\omega_{1}}^{\omega_{2}}{\frac{^{{- {({\mu_{a}h})}}\omega}}{\omega^{2}}\quad {\omega}}} = {{\int_{\omega_{1}}^{\infty}{\frac{^{{- {({\mu_{a}h})}}\omega}}{\omega^{2}}\quad {\omega}}} - {\int_{\omega_{2}}^{\infty}{\frac{^{{- {({\mu_{a}h})}}\omega}}{\omega^{2}}\quad {{\omega}.}}}}} & (10)\end{matrix}$

[0091] Using Equation (10) and changing variables on the right-hand side(RHS) of Equation (10), such as ω′=ω/ω₁ and ω″=ω/ω₂, restrictively,Equation (9) becomes: $\begin{matrix}{\varphi_{limited}^{uniform} = {\frac{S_{v}}{2\quad \mu_{s}}\lbrack {{\frac{1}{\omega_{1}}{\int_{1}^{\infty}{\frac{^{{- {({\mu_{a}\omega_{1}h})}}\omega^{\prime}}}{( \omega^{\prime} )^{2}}\quad {\omega^{\prime}}}}} - {\frac{1}{\omega_{2}}{\int_{1}^{\infty}{\frac{^{{- {({\mu_{a}\omega_{2}h})}}\omega^{\prime\prime}}}{( \omega^{\prime\prime} )^{2}}\quad {\omega^{\prime\prime}}}}}} \rbrack}} & (11)\end{matrix}$

[0092] Now using the definition of the exponential integral fromEquation (5), the gamma-ray flux for the limited polar angle case froman exponential source distribution is: $\begin{matrix}{\varphi_{limited}^{uniform} = {\frac{S_{v}}{2\quad \mu_{s}}\lbrack {\frac{E_{2}( {\mu_{a}\omega_{1}h} )}{\omega_{1}} - \frac{E_{2}( {\mu_{a}\omega_{2}h} )}{\omega_{2}}} \rbrack}} & (12)\end{matrix}$

[0093] Limited Depth Case

[0094] In addition to a reduced range of polar angle, the followingoffers a derivation for the contributions to the uncollided gamma-rayflux from a layer of soil of thickness t in cm at a depth of z_(top) incm from the soil surface. Integrating Equation (1) with respect to theazimuthal angle, φ, simplifying and making two changes of variablesresults in: $\begin{matrix}{\varphi_{total}^{uniform} = {\frac{S_{v}}{2}{\int_{0}^{\infty}{\int_{1}^{\infty}{\frac{^{{- {({{\mu_{s}z} + {\mu_{a}h}})}}\omega}}{\omega}\quad {\omega}{z}}}}}} & (13)\end{matrix}$

[0095] where ω=sec θ (sin θ dθ=dω/ω²) and z=r/ω−h(dr=ω dz). To accountfor the limited angle and depth cases, the limits of integration inEquation (13) become: $\begin{matrix}{\varphi_{layer}^{uniform} = {\frac{S_{v}}{2}{\int_{\omega_{1}}^{\omega_{2}}{\int_{ztop}^{{ztop} + t}{\frac{^{{- {({{\mu_{s}z} + {\mu_{a}h}})}}\omega}}{\omega}\quad {z}{{\omega}.}}}}}} & (14)\end{matrix}$

[0096] Integrating with respect to z, one has: $\begin{matrix}{\varphi_{layer}^{uniform} = {\frac{S_{v}}{2\quad \mu_{s}}{\int_{\omega_{1}}^{\omega_{2}}{\{ {\frac{^{{- {({{\mu_{s}z_{top}} + {\mu_{a}h}})}}\omega}}{\omega^{2}} - \frac{^{{- {({{\mu_{s}{({z_{top} + t})}} + {\mu_{a}h}})}}\omega}}{\omega^{2}}} \} {{\omega}.}}}}} & (15)\end{matrix}$

[0097] Manipulating the limits of integration and making the same changeof variables as was done in Equation (10) results in: $\begin{matrix}{\varphi_{layer}^{uniform} = {\frac{S_{v}}{2\quad \mu_{s}}\lbrack {{\frac{1}{\omega_{1}}{\int_{1}^{\infty}{\frac{^{{- {({D_{top}\omega_{1}})}}\omega^{\prime}} - ^{{- {({D_{bot}\omega_{1}})}}\omega^{\prime}}}{( \omega^{\prime} )^{2}}\quad {\omega^{\prime}}}}} - {\frac{1}{\omega_{2}}{\int_{1}^{\infty}{\frac{^{{- {({D_{top}\omega_{2}})}}\omega^{\prime\prime}} - ^{{- {({D_{bot}\omega_{2}})}}\omega^{\prime\prime}}}{( \omega^{\prime\prime} )^{2}}\quad {\omega^{\prime\prime}}}}}} \rbrack}} & (16)\end{matrix}$

[0098] where D_(top)=μ_(s) z_(top)+μ_(a)h and D_(bot)=μ_(s)(z_(top)+t)+μ_(a)h. Integrating Equation (16) yields the uncollidedgamma-ray flux due to a limited polar angle from a single layer of soilwith thickness t: $\begin{matrix}{\varphi_{layer}^{uniform} = {{\frac{S_{v}}{2\quad \mu_{s}}\lbrack {\frac{{E_{2}( {D_{top}\omega_{1}} )} - {E_{2}( {D_{bot}\omega_{1}} )}}{\omega_{1}} - \frac{{E_{2}( {D_{top}\omega_{2}} )} - {E_{2}( {D_{bot}\omega_{2}} )}}{\omega_{2}}} \rbrack}.}} & (17)\end{matrix}$

[0099] Using Equation (17), uncollided gamma-ray fluxes are calculatedfor five polar angle ranges from five soil layers with a uniform(homogeneous) ¹³⁷Cs distribution. Showing the limited angle and depthgeometries, FIG. 3 also presents the percentages of the total uncollidedgamma-ray flux, for a particular polar angle range, incident at thedetector from each soil layer. As the polar angle is increased, thepercentage of uncollided gamma-ray flux emitted from the upper soillayers increases. Therefore, large polar angle measurements can be usedto characterize radionuclide activities in the lower soil layers. Theradionuclide activities in each layer are independent and could be usedto identify appropriate depth distribution functions, if such arefinement is deemed advantageous.

[0100] Design and Collimator Geometries

[0101] The method and system of the present invention use gamma-raycollimation to limit the detector response to a small range of polarangles. A number of different cylindrically symmetric collimators arepossible and may be fabricated using lead. FIG. 4 illustrates one suchcollimator. Each collimator is designed with sloping edges that matchedthe desired polar angle. Maximizing the gamma-ray path length throughthe lead, the sloping edges minimized the contributions from thosegamma-rays emitted outside the collimated region of interest.

[0102] Simulations of uniform distribution of ¹³⁷Cs in soil are used toselect the polar angles for each collimator. For each range in polarangle, uncollided gamma-ray fluxes are calculated using Equation (17).The term “uncollided” refers to those gamma-rays that are emitted withinthe source media and do not interact in the material between theradionuclide source and the detector.

[0103] Adjusting the ranges of polar angle to yield similar uncollidedgamma-ray fluxes resulted in the following ranges: 0-34°, 34-48°,48-60°, 60-70°, and 70-80°. Assuming similar gamma-ray countingefficiencies for each collimator (which may be dependent on the actualdetector employed), qualitative information about the depth distributioncould be obtained by simply comparing the photopeak count rates fromeach collimator measurement. For instance, a photopeak count rate withthe 70-80° collimator that was significantly larger than the 0-34°measurement would indicate a greater source distribution near thesurface. Likewise, greater count rates with the 0-34° collimator wouldindicate a deeper depth distribution.

[0104] Using Equation (17), uncollided gamma-ray fluxes are calculatedfor the previously selected polar angle ranges (0-34°, 34-48°, 48-60°,60-70°, and 70-80°) from the five soil layers in FIG. 3. Depicting thelimited angle and depth geometries, FIG. 3 also presents the percentagesof the total uncollided gamma-ray flux, for a particular polar anglerange, incident on the detector from each soil layer.

[0105] For example, calculations are based on a soil layer thickness of4 cm, a detector height of 10.5 cm, a soil water content of 10%, a soilbulk density of 1.6 g cm⁻³, a linear gamma-ray attenuation coefficientfor soil at 662 keV of 0.125 cm⁻¹, and a linear gamma-ray attenuationcoefficient for air at 662 keV of 0.0001 cm⁻¹. As the polar angle isincreased, the percentage of uncollided gamma-ray flux incident from theupper soil layers increases. Therefore, large polar angle measurementscharacterize radionuclide activities in upper layers of soil.Subtracting the upper layers' contributions, the smaller polar anglemeasurements are used to determine radionuclide activities in the lowersoil layers. The radionuclide activities in each layer are independentand can be used to identify appropriate depth distribution functions, ifsuch a refinement is deemed advantageous.

[0106] The total number of radionuclide activity data points with depth(or depth parameters) can equal the number of polar angle rangessampled. Alternatively, in an oversampled case one has more angles thandepths; or in an undersampled case one can use other information toassist in the solution of the depth distribution. The cylindricalsymmetry of each collimator section increases the system's sensitivityby allowing the detector to respond to larger volumes of sourcematerial. In addition to requiring shorter count times, the collimator'scylindrical symmetry also has the effect of averaging the radionuclidedepth distribution over a much larger volume of material than thatobtained from a typical laboratory analyzed sample.

[0107]FIG. 4 shows a cross-sectional view of one collimator/detectorgeometry. A prototype lead collimator has been designed which requiresadjusting the collimator by changing individual lead pieces for eachangular measurement. To reduce the manual work required in adjusting thelead collimator in between angular measurements, a multiple anglecollimator consisting of a fixed collimator section with severaldetector locations as well as a movable collimator with a fixed detectorlocation are possible. Constructing collimator with mechanically movablesections of thick lead which are cylindrically symmetric implysignificant design challenges as well as reliability issues.

[0108] Therefore, a multiple angle collimator consisting of a fixedcollimator section with several detector locations seems moreappropriate for the system and is presented in FIG. 5. Instead of movinglead pieces for each angular measurement, the detector is simply movedto a different location within the collimator shaft. In regard tocharacterizing the source material directly beneath the system (smallerpolar angles), two possibilities have been presented. Both require theremoval of the lowest (on-axis) section of the lead collimator.

[0109]FIG. 6 suggests the addition of another lead section while thedetector remains in the lowest location, and FIG. 7 suggests moving thedetector to new upper location without requiring the placement of newlower lead section. The main disadvantage of the new upper detectorlocation (FIG. 7) is that a longer detector cryostat would be required.Initial calculations suggest that four detector locations (FIG. 7)requires a typical portable detector cryostat to be lengthened byroughly 10 cm. Therefore, with a standard length cryostat, threedetector positions and three removable lead collimator sections at thebottom of the collimator would be required to allow for five differentangular measurements.

[0110] Other collimator/detector geometries are shown in FIGS. 8a-8 d.FIG. 8a depicts a movable collimator with a fixed detector. However,constructing a collimator with mechanically movable sections of thicklead that are cylindrically symmetric implies significant designchallenges. FIG. 8b shows a dual detector design with movable on-axiscollimation, which allows the system to focus in on a particular depth.FIG. 8c displays a system where the detector can be moved with respectto a fixed cylindrical collimator or plate (or the collimator could bemoved with respect to a fixed detector) to obtain the angularinformation. FIG. 8d shows a simple pivoting design as an alternative tothe vertical movements of FIG. 8c.

[0111] Limitations of any in situ gamma-ray spectrometry system dependon the specific radionuclide of interest. Depth information forradionuclides which only emit gamma-rays at very low energies (<100 keV)will be limited to the shallower layers of soil due to the increasedself-attenuation of the soil. However, the system design parameterscould be modified to specifically obtain greater depth information forlow-energy gamma-ray emitters if deemed necessary. At the other extreme,radionuclides which emit gamma-rays at high energies (>2 MeV) would notimpose such a limitation because the reduced detection efficiency forhigh energy gamma-rays would tend to be offset by a reduction inself-attenuation.

[0112] As an alternative to moving a single crystal detector to adifferent location for each measurement in FIGS. 5-7, a multipledetector system can simultaneously acquire data from several angles.This has the significant advantage of improving detection efficiency andtherefore decrease measurement times. CdZnTe detector advancements allowfor the fabrication of customized and compact detector arrays within thetight confines of the collimator. The detectors inserted in thecollimator could be operated to give xy spatial dependence over the soilplane. Any other semiconductor besides CdZnTe, scintillator or otherdetectors or detector materials may also be used.

[0113] Referring to FIG. 9, a combination of two types of detectorshaving different energy resolution, sensitivity or other propertiesimprove positional spectroscopic determinations. One way of doing thisis to have a central detector having a high energy resolution, such asintrinsic germanium, surrounded by spectroscopic detectors havinggreater sensitivities (or which can be reasonably manufactured in largerpieces).

[0114] The inner detector, perhaps having a larger field of view thanthe outer detectors, determine (more precisely than the other, lowerenergy-resolution detectors) the average spectral fingerprint of theoverall area, while providing information useful for analyzing the datafrom the other detectors.

[0115] The outer detectors provide information about the spatialdistribution of the ionizing radiation sources; any spectral informationfrom these detectors could also be utilized. The hybrid detectors couldalternatively be manufactured in a curved geometry of some type.

[0116] As shown in FIG. 9, a ring of smaller CdZnTe devices can bewrapped around a core HPGe device to produce a compound gamma-rayspectrometer that is position sensitive. For instance, segmented ringsof CdZnTe detectors are arranged around a large coaxial HPGe detector togive both radial position location (CdZnTe devices) and very high energyresolution (HPGe device). The bottom HPGe detector can have a segmentedCdZnTe array on a xy plane to give further information as to the spatialdistribution of source emissions directly beneath the device. The higherabsorption efficiencies of the CdZnTe devices reduces the volumerequirements, in which the CdZnTe devices should not interfere with theHPGe device performance. Properly placed collimator openings allow formeasurements with and without the CdZnTe devices blocking the centralHPGe devices. Miniaturized preamplifiers and readout electronics allowfor the straightforward implementation of such a concept. Thecombination of spatial and depth distributions represents the first stepin determining three-dimensional data of radionuclide distributions.Obviously, other detector arrangements may be provided. For example, oneor more of the satellite detectors could be a single ring of positionaldetectors. The position of the higher energy resolution detectors andthe higher spatial resolution detectors could be reversed.

[0117] Current in situ methods only have the ability to fit simple depthdistributions and provide no spatial information. Therefore, theproposed system's ability to obtain three-dimensional distribution datarepresents an overwhelming advantage for radionuclide characterizationsin soil.

[0118] While the best mode for carrying out the invention has beendescribed in detail, those familiar with the art to which this inventionrelates will recognize various alternative designs and embodiments forpracticing the invention as defined by the following claims.

What is claimed is:
 1. A method for determining depth distribution ofradiation-emitting material located in a source medium, the methodcomprising: detecting radiation emitted by the material within selectedranges of polar angles relative to a detector axis which issubstantially perpendicular to an outer surface of the source medium toproduce a plurality of corresponding electrical signals; and processingthe plurality of electrical signals to obtain the depth distribution ofthe radiation-emitting material in the source medium.
 2. The method ofclaim 1 wherein the radiation includes x-ray emissions.
 3. The method ofclaim 1 wherein the radiation includes gamma-ray emissions.
 4. Themethod of claim 1 wherein the material is radionuclides.
 5. The methodof claim 1 further comprising energizing the material so that thematerial emits the radiation.
 6. The method of claim 1 wherein thesource medium is soil.
 7. The method of claim 1 wherein the sourcemedium includes building materials.
 8. The method of claim 7 wherein thebuilding materials include concrete.
 9. The method of claim 7 whereinthe building materials include steel.
 10. The method of claim 1 whereinthe source medium is an airborne plume.
 11. The method of claim 1wherein the step of detecting is at least partially performed with adetector having intrinsic efficiency and angular response and whereinthe step of processing processes data representing the intrinsicefficiency and the angular response with the electrical signals toobtain the depth distribution.
 12. A system for determining depthdistribution of radiation-emitting material located in a source medium,the system comprising: at least one detector assembly for detectingradiation emitted by the material within selected ranges of polar anglesrelative to a detector axis which is substantially perpendicular to anouter surface of the source medium to produce a plurality ofcorresponding electrical signals; and a signal processor for processingthe plurality of electrical signals to obtain the depth distribution ofthe radiation-emitting material in the source medium.
 13. The system ofclaim 12 wherein the at least one detector assembly includes a radiationdetector and a radiation shield which surrounds the radiation detector,wherein the at least one detector assembly is adjustable to allow theradiation detector to detect radiation within the selected ranges of thepolar angles and the radiation shield substantially blocks radiationoutside the selected ranges of the polar angles.
 14. The system of claim13 wherein the shield is a collimator.
 15. The system of claim 14wherein the collimator is cylindrically symmetrical.
 16. The system ofclaim 13 wherein the collimator includes a plurality of collimatorpieces which can be assembled into a plurality of geometric arrangementscorresponding to the ranges of polar angles.
 17. The system of claim 14wherein the collimator is adjustable into a plurality of geometricarrangements corresponding to the ranges of polar angles.
 18. The systemof claim 13 wherein the at least one detector assembly includes aradiation spectrometer.
 19. The system of claim 12 wherein the at leastone detector assembly includes at least one of an array of detectors, aposition-sensitive detector and a scanning detector.
 20. The system ofclaim 14 wherein the collimator is movable relative to the detector. 21.The system of claim 20 wherein the collimator includes at least onecollimator piece which is pivotally movable relative to the detector.22. The system of claim 13 including a pair of detector assemblies toallow the system to focus at a selected depth of the source medium. 23.The system of claim 20 wherein the collimator is linearly movablerelative to the detector.
 24. The system of claim 23 wherein thecollimator is cylindrically symmetrical about the detector.
 25. Thesystem as claimed in claim 13 wherein the at least one detector assemblyhas a relatively narrow field of view that is capable of being directedat a desired polar angle for a measurement and is rotatable about thedetector axis.
 26. A radiation detector system comprising: at least onecentral radiation detector for converting ionizing radiation into afirst signal; at least one satellite radiation detector positionedadjacent the at least one central radiation detector for convertingionizing radiation into at least one second signal; and at least oneradiation shield disposed adjacent the at least one satellite radiationdetector to substantially block ionizing radiation originating outside afield of view of the at least one satellite radiation detector whereinthe first signal and the at least one second signal represent a spectralfingerprint of an area and spatial distribution of an ionizing radiationsource within the area.
 27. The system as claimed in claim 26 whereinthe at least one satellite radiation detector is a spectroscopicradiation detector.
 28. The system as claimed in claim 26 wherein theionizing radiation includes gamma rays and wherein the system is aposition-sensitive, compound gamma ray spectrometer.
 29. The system asclaimed in claim 26 wherein the at least one central radiation detectorincludes a semiconductor substrate.
 30. The method as claimed in claim 1wherein the method is either an oversampled or an undersampled methodwherein the number of polar angles is greater than or less than thenumber of depths, respectively, and wherein in the undersampled methodother information is processed with the electrical signals to obtain thedepth distribution.
 31. The invention as claimed in claim 1 or claim 12wherein the depth distribution is a spatially-uniform depthdistribution.
 32. The system as claimed in claim 13 where the entiredetector assembly is rotatable about a normal of the source surface andwherein the entire detector assembly has a narrow field of view and afixed-polar angle.
 33. The system as claimed in claim 26 wherein the atleast one satellite detector is a positional detector.
 34. The method asclaimed in claim 1 further comprising providing material which deflectsthe radiation.